It’s important to know the difference between an
equation
and an
expression
. An equation
contains an = symbol and an expression does not.
A number that makes an equation true when substituted for the variable is called a solution and
it is said to satisfy the equation.
The solution set of an equation is the set of all numbers that make the equation true.
To solve an equation means to find all values of the variable that make the equation true.
Equations with the same solutions are called
equivalent equations
.
Adding the same number to both sides of an equation does not change its solution.
For any real numbers a, b, and c,
If a=b, then a+c = b+c
We solve equations by writing a series of steps that result in an equivalent equation of the form
X = a number
or
a number = x
We say the variable is isolated on one side of the equation. Isolated means alone or by itself.
Subtracting the same number from both sides of an equation does not change its solution.
For any real numbers a, b, and c,
If a=b, then a-c=b-c

Multiplication Property of Equality
Multiplying both sides of an equation by the same nonzero number does not change its solution
For any real numbers a, b, and c, where c is not 0
If a=b, then ca= cb
Division property of equality
Dividing both sides of an equation by the same nonzero number does not change its solution.
For any real numbers a, b, and c, where c is not 0,
If a=b, then a/c = b/c
2.2a More about Solving Equations (Pages 112-116
)
Objective:
1.
Use more than one property of quality to solve equations
2.
Simplify expressions to solve equations
A linear equation in one variable can be written in the form
Ax+b=c
Recall that:
Subtraction undoes addition
Addition undoes subtraction
Division undoes multiplication
Multiplication undoes division
When solving an equation, if variables appear on both sides, we can use the addition (or
subtraction) property of equality to get all variable terms on one side and all constant terms on
the other.

WEEK 4
2.2 More about solving equations Obj 3-4 Pages 116-119
If an equation contains decimals, it is often convenient to multiply both sides by a power of 10
to change the decimals in the equation to integers.
Recall that multiplying a decimal by 10 moves the decimal point 1 place to the right, multiplying
it by 100 moves it 2 places to the right, and so on.
When we write the decimals in the original equation as fractions, it becomes more apparent
why it is helpful to multiply both sides by the LCD, 100.
Strategy for solving linear equations in one variable
1.
Clear the equation of fractions or decimals
: multiply both sides by the LCD to clear
fractions or multiply both sides by a power of 10 to clear decimals
2.
Simplify each side of the equations
: use the distributive property to remove
parentheses, and then combine like terms on each side.